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Theorem 19.9t 2022
Description: A closed version of 19.9 2023. (Contributed by NM, 13-May-1993.) (Revised by Mario Carneiro, 24-Sep-2016.) (Proof shortened by Wolf Lammen, 30-Dec-2017.) (Proof shortened by Wolf Lammen, 14-Jul-2020.)
Assertion
Ref Expression
19.9t (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))

Proof of Theorem 19.9t
StepHypRef Expression
1 id 22 . . 3 (Ⅎ𝑥𝜑 → Ⅎ𝑥𝜑)
2119.9d 2021 . 2 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
3 19.8a 1988 . 2 (𝜑 → ∃𝑥𝜑)
42, 3impbid1 210 1 (Ⅎ𝑥𝜑 → (∃𝑥𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wb 191  wex 1692  wnf 1696
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1698  ax-4 1711  ax-5 1789  ax-6 1836  ax-7 1883  ax-10 1965  ax-12 1983
This theorem depends on definitions:  df-bi 192  df-ex 1693  df-nf 1697
This theorem is referenced by:  19.9  2023  19.9hOLD  2026  19.9dOLD  2027  19.21t  2039  19.23tOLD  2045  spimt  2144  sbft  2262  vtoclegft  3142  bj-cbv3tb  31499  bj-spimtv  31506  bj-sbftv  31557  bj-equsal1t  31606  bj-19.21t  31614  19.9alt  32771
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